Patrick Schmidt, M.Sc.
Room 114
Phone: +49 241 8021803
Fax: +49 241 8022899
Email: patrick.schmidt@cs.rwth-aachen.de


Distortion-Minimizing Injective Maps Between Surfaces

Patrick Schmidt, Janis Born, Marcel Campen, Leif Kobbelt
SIGGRAPH Asia 2019

The problem of discrete surface parametrization, i.e. mapping a mesh to a planar domain, has been investigated extensively. We address the more general problem of mapping between surfaces. In particular, we provide a formulation that yields a map between two disk-topology meshes, which is continuous and injective by construction and which locally minimizes intrinsic distortion. A common approach is to express such a map as the composition of two maps via a simple intermediate domain such as the plane, and to independently optimize the individual maps. However, even if both individual maps are of minimal distortion, there is potentially high distortion in the composed map. In contrast to many previous works, we minimize distortion in an end-to-end manner, directly optimizing the quality of the composed map. This setting poses additional challenges due to the discrete nature of both the source and the target domain. We propose a formulation that, despite the combinatorial aspects of the problem, allows for a purely continuous optimization. Further, our approach addresses the non-smooth nature of discrete distortion measures in this context which hinders straightforward application of off-the-shelf optimization techniques. We demonstrate that, despite the challenges inherent to the more involved setting, discrete surface-to-surface maps can be optimized effectively.

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author = {Schmidt, Patrick and Born, Janis and Campen, Marcel and Kobbelt, Leif},
title = {Distortion-Minimizing Injective Maps Between Surfaces},
journal = {ACM Transactions on Graphics},
issue_date = {November 2019},
volume = {38},
number = {6},
month = nov,
year = {2019},
articleno = {156},
url = {https://doi.org/10.1145/3355089.3356519},
doi = {10.1145/3355089.3356519},
publisher = {ACM},
address = {New York, NY, USA},

Interactively Controlled Quad Remeshing of High Resolution 3D Models

Hans-Christian Ebke, Patrick Schmidt, Marcel Campen, Leif Kobbelt
SIGGRAPH Asia 2016

Pa­ra­met­ri­za­tion based methods have recently become very popular for the generation of high quality quad meshes. In contrast to previous approaches, they allow for intuitive user control in order to accommodate all kinds of application driven constraints and design intentions. A major obstacle in practice, however, are the relatively long computations that lead to response times of several minutes already for input models of moderate complexity. In this paper we introduce a novel strategy to handle highly complex input meshes with up to several millions of triangles such that quad meshes can still be created and edited within an interactive workflow. Our method is based on representing the input model on different levels of resolution with a mechanism to propagate pa­ra­met­ri­za­tions from coarser to finer levels. The major challenge is to guarantee consistent pa­ra­met­ri­za­tions even in the presence of charts, transition functions, and singularities. Moreover, the remaining degrees of freedom on coarser levels of resolution have to be chosen carefully in order to still achieve low distortion pa­ra­met­ri­za­tions. We demonstrate a prototypic system where the user can interactively edit quad meshes with powerful high-level operations such as guiding constraints, singularity repositioning, and singularity connections.

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author = {Ebke, Hans-Christian and Schmidt, Patrick and Campen, Marcel and Kobbelt, Leif},
title = {Interactively Controlled Quad Remeshing of High Resolution 3D Models},
journal = {ACM Trans. Graph.},
issue_date = {November 2016},
volume = {35},
number = {6},
month = nov,
year = {2016},
issn = {0730-0301},
pages = {218:1--218:13},
articleno = {218},
url = {http://doi.acm.org/10.1145/2980179.2982413},
doi = {10.1145/2980179.2982413},
acmid = {2982413},
publisher = {ACM},
address = {New York, NY, USA},

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